Integration tests are very important and in many cases mandatory. I'd argue though unit tests with good coverage are more important. The latter helps you make sure your application has the correct output. Nothing worst than having a piece of software you think is working and silently introducing errors. The former (integration tests) makes sure your application starts and probably works in some scenarios.

With docker and containers, integration testing is easier than ever.

I've written a very simple integration testing tool (a quick hack to be honest) that executes commands, checks their exit code, the output through regexp, etc and produces a nice html report.

https://github.com/landoop/coyote

Originally written for testing some configuration tools and scripts, we quickly found a use for it for our Kafka connector collection (Stream Reactor). Our connector integration tests are at github as well:

https://github.com/Landoop/kafka-connectors-tests

Obviously unit tests make sure that the connectors work as expected. Integration tests catch simpler errors that can be showstoppers. For example an internally renamed configuration option that didn't trickle down to the configuration parser, class shadowing issues between the connectors, unexpected errors in logs that the developers should check out etc. As the tests are written by people who don't do development, they also expose problems in the documentation. In some cases they provide us an easy way to quickly run locally a connector and catch some issues manually, like extensive CPU usage or way too much logging (e.g a function with a log statement was inside a loop that run hundreds or thousands of times per second).

It gives us confidence in what we ship with every release.